Remove from heat, and let cool 10 minutes. Put half of stock mixture and about a fourth of the mushrooms into a blender or food processor. Add half-and-half and the starch or flour. Process until the mushrooms are broken up, and the mixture is fairly lump-free. Put mixture back into the stockpot, with remaining stock and mushrooms.

Gently reheat, over low heat. Stir in the butter. Season with salt and pepper.